1 3 ? 7 9 11

1 3 5 7 9 11 13

Arithmetic Series an = a1 + (n – 1)d

Imagine this pyramid of logs continues on with it’s last row having 200 logs.

Imagine this pyramid of logs continues on with it’s last row having 200 logs. What are the first 10 terms in this sequence (the first 10 rows)?

Imagine this pyramid of logs continues on with it’s last row having 200 logs. What are the first 10 terms in this sequence (the first 10 rows)? What is the common difference?

What would be the formula to figure out the nth term in the sequence (the nth row)?

What would be the formula to figure out the nth term in the sequence (the nth row)? an = a1 + (n – 1)d

What would be the formula to figure out the nth term in the sequence (the nth row)? an = a1 + (n – 1)d a1 = 2, d = 2

What would be the formula to figure out the nth term in the sequence (the nth row)? an = 2 + (n – 1)2 an = 2 + 2n –2 an = 2n

How many logs would be in the 76th row?

How many logs would be in the 76th row? an = 2n a76 = 2(76) = 152

Denote the common difference of d First four terms: a1, a2 = a1 + d, a3 = a2 + d = (a1 + d) + d = a1 + 2d, a4 = a3 + d = (a2 + d) + d = a1 + 3d

Denote the common difference of d First four terms: a1, a2 = a1 + d, a3 = a2 + d = (a1 + d) + d = a1 + 2d, a4 = a3 + d = (a2 + d) + d = a1 + 3d Generalize a formula for the nth term of arithmetic sequence.

Denote the common difference of d First four terms: a1, a2 = a1 + d, a3 = a2 + d = (a1 + d) + d = a1 + 2d, a4 = a3 + d = (a1 + d) + d = a1 + 3d Generalize a formula for the nth term of arithmetic sequence. an = a1 + (n – 1)d, for any n that greater than 1.

Determine whether the sequence is arithmetic Determine whether the sequence is arithmetic. If it is, find the common difference & formula for nth term: 1. 2, 12, 22, 32, 42, … 2. 25, 23, 21, 19, … 3. -17, -12, -7, -2, 3, 8… 4. an = 4 + 3n

Determine whether the sequence is arithmetic Determine whether the sequence is arithmetic. If it is, find the common difference & formula for nth term: 1. 2, 12, 22, 32, 42, … d = 10, an = 10n - 8 2. 25, 23, 21, 19, … d = -2, an = -2n + 27 3. -17, -12, -7, -2, 3, 8… d = 5, an = 5n - 22 4. an = 4 + 3n

Determine whether the sequence is arithmetic Determine whether the sequence is arithmetic. If it is, find the common difference & formula for nth term: 1. 2, 12, 22, 32, 42, … d = 10, an = 10n - 8 2. 25, 23, 21, 19, … d = 25, an = -2n + 27 3. -17, -12, -8, -3, 2, 7… d = -17, an = 5n - 22 4. an = 4 + 3n d = 7, an = 7 + 3(n-1)

2 4 8 ? 32 128

2 4 8 16 32 64 128

Geometric Series an = a1 r(n – 1)

This morning, the cast list for the Crucible came out.. The first 3 people to see the list each texted 5 other friends to tell them the news. Those recipients each texted 5 more friends to tell them the news. How many people know the cast list is out?

Denote the common ratio d First four terms: a1, a2 = a1r, a3 = (a1r)r = a1r2 a4= (a1r2)r = a1r3

Denote the common ratio d First four terms: a1, a2 = a1r, a3 = (a1r)r = a1r2 a4= (a1r2)r = a1r3 Generalize a formula for the nth term of arithmetic sequence.

Denote the common ratio d First four terms: a1, a2 = a1r, a3 = (a1r)r = a1r2 a4= (a1r2)r = a1r3 Generalize a formula for the nth term of arithmetic sequence. an = a1 r(n – 1)

Determine whether the sequence is geometric Determine whether the sequence is geometric. If it is, find the common ratio & formula for nth term: 1. 3, 6, 10, 15, … 2. 1, -2, 4, -8, … 3. 1, ½, ¼, ⅛, … 4. an = 2(⅔)(n – 1)

Determine whether the sequence is geometric Determine whether the sequence is geometric. If it is, find the common ratio & formula for nth term: 1. 3, 6, 10, 15, … not geometric sequence 2. 1, -2, 4, -8, … r = -2, an = 1(-2)(n – 1) 3. 1, ½, ¼, ⅛, … r = ½, an = 1(½)(n – 1) 4. an = 2(⅔)(n – 1)

Determine whether the sequence is geometric Determine whether the sequence is geometric. If it is, find the common ratio & formula for nth term: 1. 3, 6, 10, 15, … not geometric sequence 2. 1, -2, 4, -8, … r = -2, an = 1(-2)(n – 1) 3. 1, ½, ¼, ⅛, … r = ½, an = 1(½)(n – 1) 4. an = 2(⅔)(n – 1) r = ⅔, an = 2(⅔)(n – 1)

Determine whether the sequence is arithmetic or geometric Determine whether the sequence is arithmetic or geometric. If it is, find the formula for nth term: 1. 12, 15, 18, 21, 24, … 2. 3, 6, 12, 24, 48 … 3. 2, 6, 18, 54, 162 … 4. -5, -1, 3, 7, 11 ...

Find the 12rd term for the 3rd & 4th sequence 3. 2, 6, 18, 54, 162 … a12 = 2(3)(12 – 1) = 2(3)(11) = 354,294 4. -5, -1, 3, 7, 11 … a12 = 4(12) - 9 = 39